“He should resign or the reconstituted board should let him go,” David Dreman, chairman of Dreman Value Management Inc., which holds about 1 million Chesapeake shares, told Bloomberg. “This company’s got to get its credibility back. As long as you have a guy like Aubrey there, I don’t think we’re going to get the credibility back.”

"Accountability is what it's all about, and it's time for a change," activist investor Gerald Armstrong said at the meeting, according to Reuters. "It's likely you (McClendon) might not be with us next year."

At the annual meeting, less than one-quarter of shareholders supported the re-election of two directors, V. Burns Hargis, president of Oklahoma State University, and Richard Davidson, a former CEO of Union Pacific Corp., Reuters reports. Hargis and Davidson then tendered their resignations from the board of the Oklahoma City-based company.

However, the company said in a June 8 statement that it would decide later whether to accept the resignations of the two, who are leading a probe of McClendon’s loans, Bloomberg reports.

Additionally, only 20 percent of shareholders at the meeting supported Chesapeake’s executive officer compensation program, though that advisory measure vote is not binding.

Since April, Chesapeake has faced scrutiny from investors and the U.S. Securities and Exchange Commission after revelations about a controversial compensation plan in which McClendon was able to invest in the company's wells.

Earlier this month, Chesapeake agreed to replace four of its nine board members with those selected by investors Southeastern Asset Management and Carl Icahn. Additionally, McClendon will relinquish his chairmanship once a non-executive chairman has been appointed to replace a retiring board member. Chesapeake estimates its new board will be in place by June 22.

Chesapeake's major competitor is Irving-based Exxon Mobil Corp. (NYSE: XOM), which has a significant presence in Houston.